Granular Matter

, 9:337 | Cite as

Development of micromechanical models for granular media

The projection problem
  • Stuart D. C. Walsh
  • Antoinette Tordesillas
  • John F. Peters


Micromechanical analysis has the potential to resolve many of the deficiencies of constitutive equations of granular continua by incorporating information obtained from particle-scale measurements. The outstanding problem in applying micromechanics to granular media is the projection scheme to relate continuum variables to particle-scale variables. Within the confines of a projection scheme that assumes affine motion, contact laws based on binary interactions do not fully capture important instabilities. Specifically, these contact laws do not consider mesoscale mechanics related to particle group behaviour such as force chains commonly seen in granular media. The implications of this are discussed in this paper by comparison of two micromechanical constitutive models to particle data observed in computer simulations using the discrete element method (DEM). The first model, in which relative deformations between isolated particle pairs are projected from continuum strain, fails to deliver the observed behaviour. The second model accounts for the contact mechanics at the mesoscale (i.e. particle group behaviour) and, accordingly, involves a nonaffine projection scheme. In contrast with the first, the second model is shown to display strain softening behaviour related to dilatancy and produce realistic shear bands in finite element simulations of a biaxial test. Importantly, the evolution of microscale variables is correctly replicated.


Micromechanics Micropolar Thermomechanics Mesoscale 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Stuart D. C. Walsh
    • 1
  • Antoinette Tordesillas
    • 1
  • John F. Peters
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia
  2. 2.US Army Corps of EngineersEngineer Research and Development CenterVicksburgUSA

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